{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 从高维数据向低维数据的映射"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.empty((100, 2))\n",
    "X[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 10., size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Wall time: 3.29 s\nWall time: 3.28 s\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PCA(n_components=2)"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "from playML.PCA import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "%time pca.fit(X, k=100)\n",
    "%time pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 0.79617135,  0.60507121],\n       [-0.60507121,  0.79617135]])"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PCA(n_components=1)"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_reduction = pca.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 1)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "X_reduction.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_restore = pca.inverse_transform(X_reduction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 2)"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "X_restore.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], color='b', alpha=0.5)\n",
    "plt.scatter(X_restore[:,0], X_restore[:,1], color='r', alpha=0.5)\n",
    "plt.show()\n",
    "# 降维恢复之后只能恢复到主成分轴上"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### scikit-learn中的PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,\n    svd_solver='auto', tol=0.0, whiten=False)"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.80276638, -0.59629367]])"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "# 因为计算方法不一样(严密的数学求解)，所以轴方向不一样，但是无所谓\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_reduction = pca.transform(X)\n",
    "X_restore = pca.inverse_transform(X_reduction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], color='b', alpha=0.5)\n",
    "plt.scatter(X_restore[:,0], X_restore[:,1], color='r', alpha=0.5)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.8 64-bit ('anaconda': conda)",
   "language": "python",
   "name": "python36864bitanacondaconda085db2e8b14649f4b32196068f7124e9"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}